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Abstract This paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds. 

Abstract In this study, we describe a method to construct a correlation map that captures the evolution of species‐specific dynamic information through the spatial correlation of high‐dimensional time‐series molecular dynamics (MD) simulation dataset for a series of borosilicate glasses. The correlation is based on ‘displacement’ between a pair of atomic configurations determined by the root mean square distance (RMSD) metric. We implement the correlation map as a quantitative visualization tool that provides a compressed representation of a high‐dimensional molecular dynamics dataset to inspect various physical aspects and capture distinct atomic dynamics—from large fluctuations to small local oscillations—for high‐temperature melt, linear cooling, and low‐temperature equilibration processes during molecular dynamics simulation of glasses. We capture species‐specific dynamics using this method that show different cooling dynamics for different glass formers and modifiers, especially the onset of slow dynamics and the variation of atomic dynamics at high temperatures. Furthermore, we show that the species‐specific atomic dynamics have structural origins that depend on the composition of the simulated borosilicate glasses. The correlation map serves as a visualization tool to rapidly survey changes in atomic configurations during different simulation conditions.